An Isoperimetric Inequality for Planar Triangulations

An Isoperimetric Inequality for Planar Triangulations

We prove a discrete analogue to a classical isoperimetric theorem of Weil for surfaces with non-positive curvature. It is shown that hexagons in the triangular lattice have maximal volume among all sets of a given boundary in any triangulation with minimal degree 6.

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Veröffentlicht in:Discrete & computational geometry 2018-06, Vol.59 (4), p.802-809
Hauptverfasser: Angel, Omer, Benjamini, Itai, Horesh, Nizan
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Computational Mathematics and Numerical Analysis
Curvature
Hexagons
Mathematics
Mathematics and Statistics
Triangulation
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Beschreibung
Zusammenfassung:We prove a discrete analogue to a classical isoperimetric theorem of Weil for surfaces with non-positive curvature. It is shown that hexagons in the triangular lattice have maximal volume among all sets of a given boundary in any triangulation with minimal degree 6.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-017-9942-3